The sum of two numbers is $52$, and their difference is $20$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 52}$ ${x-y = 20}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 72 $ $ x = \dfrac{72}{2} $ ${x = 36}$ Now that you know ${x = 36}$ , plug it back into $ {x+y = 52}$ to find $y$ ${(36)}{ + y = 52}$ ${y = 16}$ You can also plug ${x = 36}$ into $ {x-y = 20}$ and get the same answer for $y$ ${(36)}{ - y = 20}$ ${y = 16}$ Therefore, the larger number is $36$, and the smaller number is $16$.